Dirichlet boundary value problem for a system of n second order asymptotically asymmetric differential equations

Date

2018-01-24

Authors

Gritsans, Armands
Sadyrbaev, Felix
Yermachenko, Inara

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Publisher

Texas State University, Department of Mathematics

Abstract

We consider systems of the form x1″ + g1(x1) = h1(x1, x2,..., xn), x2″ + g2(x2) = h2(x1, x2,..., xn), ... xn″ + gn(xn) = hn(x1, x2,..., xn) along with the boundary conditions x1(0) = x2(0) = ∙∙∙ = xn(0) = 0 = x1(1) = x2(1) = ∙∙∙ = xn(1). We assume that right sides are bounded continuous functions, and satisfy hi(0, 0,..., 0) = 0. Also we assume that gi(xi are asymptotically asymmetric functions. By using vector field rotation theory, we provide the existence of solutions.

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Keywords

Dirichlet boundary value problem, Rotation of vector field, Asymptotically asymmetric nonlinearities, Index of isolated singular point, Fucik spectrum

Citation

Gritsans, A., Sadyrbaev, F., & Yermachenko, I. (2018). Dirichlet boundary value problem for a system of n second order asymptotically asymmetric differential equations. <i>Electronic Journal of Differential Equations, 2018</i>(35), pp. 1-16.

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Attribution 4.0 International

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